A hollow conducting sphere of radius `R` has a charge `(+Q)` on its surface. What is the electric potential within the
sphere at a distance `r = (R )/(3)` from its centre ?

Options

A. Zero
B. `(1)/(4pi epsilon_(0))(Q)/(r )`
C. `(1)/(4pi epsilon_(0))(Q)/(R )`
D. `(1)/(4pi epsilon_(0))(Q)/(r^(2)) `

Explanation

To solve the problem, we need to find the electric potential at a distance \( r = \frac{R}{3} \) from the center of a hollow conducting sphere of radius \( R \) with a charge \( +Q \) on its surface.

### Step-by-Step Solution:

1. **Understanding the Properties of a Hollow Conducting Sphere**:
- A hollow conducting sphere has the property that the electric field inside the sphere is zero. This means that there are no electric field lines within the hollow region of the sphere.

2. **Electric Potential Inside the Sphere**:
- Since the electric field inside the hollow conducting sphere is zero, the electric potential throughout the interior of the sphere is constant. This constant potential is equal to the potential at the surface of the sphere.

3. **Calculating the Surface Potential**:
- The electric potential \( V \) at the surface of a charged sphere is given by the formula:
\[ V = k \frac{Q}{R} \]
where \( k = \frac{1}{4 \pi \epsilon_0} \).

4. **Substituting the Values**:
- Therefore, the potential at the surface of the sphere is:
\[ V = \frac{1}{4 \pi \epsilon_0} \frac{Q}{R} \]

5. **Conclusion**:
- Since the potential inside the sphere is uniform and equal to the surface potential, the electric potential at a distance \( r = \frac{R}{3} \) from the center of the sphere is also:
\[ V = \frac{1}{4 \pi \epsilon_0} \frac{Q}{R} \]

### Final Answer:
The electric potential within the sphere at a distance \( r = \frac{R}{3} \) from its center is:
\[ V = \frac{1}{4 \pi \epsilon_0} \frac{Q}{R} \]